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Cayley diagram

A4×D11 #63165

order264
isoclinismisoclinic class of A4×D11
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C2

Aliases

direct productA4×D11
unambiguous semidirect productC11⋊(C2×A4)
unambiguous semidirect product(C22×D11)⋊C3

Splittings

Fitting, socle, derivedC22×C11 ⋊ C2×C3
HallC22×D11 ⋊ C3
SylowC11 ⋊ C2×A4

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC22×C11C2×C3
LCSG ▷ C22×C11
UCSC1

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 15
transitive degreeμt(G) = 44

A minimal faithful permutation representation — 2 generators on 15 points:

(2,3)(4,5)(6,7)(8,9)(10,11)(13,14,15);(1,2,4,6,8,10,11,9,7,5,3)(12,15)(13,14)

Conjugacy classes & character table

28 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD11×S4, C2×A4×D11, C3×A4×D11, …
maximal normal subgroup ofD11×S4, C2×A4×D11, C3×A4×D11, …
maximal quotient ofC11⋊(#41⋊C3), D11×SL(2,𝔽3), A4×Dic11, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(264, 33);